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IMAGE REGISTRATION TECHNIQUES
FOR MEDICAL IMAGES
Thesis submitted in partial fulfilment of the requirements for the degree
of
Master of Technology
in
Electronics and Instrumentation Engineering
by
Sangeeta Sahu
Roll No: 212EC3379
Department of Electronics & Communication Engineering
National Institute of Technology Rourkela
Rourkela, Odisha-769008
May 2014
IMAGE REGISTRATION TECHNIQUES
FOR MEDICAL IMAGES
Thesis submitted in partial fulfilment of the requirements for the degree
of
Master of Technology
in
Electronics and Instrumentation Engineering
by
Sangeeta Sahu
Roll No: 212EC3379
Under the Supervision of
Prof. Umesh Chandra Pati
Department of Electronics & Communication Engineering
National Institute of Technology Rourkela
Rourkela, Odisha-769008
May 2014
Dedicated
To
My Teachers,
Family and Friends
Department of Electronics & Communication Engineering
National Institute of Technology, Rourkela
CERTIFICATE
This is to certify that the Thesis Report entitled ― “Image Registration Techniques For
Medical Images” submitted by Miss. SANGEETA SAHU bearing roll no. 212EC3379 in
partial fulfilment of the requirements for the award of Master of Technology in Electronics
and Communication Engineering with specialization in “Electronics and Instrumentation
Engineering” during session 2012-2014 at National Institute of Technology, Rourkela is
authentic work carried out by him under my supervision and guidance.
To the best of my knowledge, the matter embodied in the thesis has not been submitted to any
other University / Institute for the award of any Degree or Diploma.
Prof. Umesh Chandra Pati
Place: Associate Professor
Date: Dept. of Electronics and Comm. Engineering
National Institute of Technology
Rourkela-769008
v
ACKNOWLEDGEMENT
I would sincerely like to acknowledge the support of my guide Prof. Umesh C.Pati, whose
guidance and support helped me at every step of the research done as well as thesis writing.
He always made himself available for all our doubts and also took every possible care
regarding the facilities in Virtual and Intelligent Instrumentation Laboratory. He encouraged
me all the time and kept me motivated and inspired. He helped me to overcome all hurdles in
my work. It is always my pleasure to interact with him on any topic.
I am grateful to Mr. Sankat and Subhranshu, for their support, guidance and innovative
suggestions. I would also like to thank Achala Madam for her support.
All my lab mates Sandeep, Shishir, Goverdhan and Ranjan made this task more interesting by
discussing various topics and suggesting new ideas. Also, I would thank all my mates of the
specialization of Electronics and Communication Engineering for their constant support and
encouragement.
Most importantly, I would thank my parents and my siblings for always being on my side and
supporting me with their blessings.
DATE: ROLL NO: 212EC3379
PLACE: Dept. of ECE
NIT, Rourkela
vi
ABSTRACT
Image registration is a primary step in many real time image processing applications.
Registration of images is the bringing of two or more images into a single coordinate system
for its subsequent analysis. It is sometimes called image alignment. It is widely used in
remote sensing, medical imaging, target recognition using multi-sensor fusion, monitoring of
usage of a particular land using satellite images, images alignment obtained from different
medical modalities for diagnosis of diseases. It is an important step in the field of image
fusion and image mosaicing.
In this research work, approaches for image registration are proposed. The image registration
methods can be grouped into two classes. One is intensity based method which is based on
gray values of the pair of images and the second one is based on image feature which is done
by obtaining some features or landmarks in the images like points, lines or surfaces. Edges in
the images can be detected very easily in the images. Thus, using these edges some features
can be obtained by which we can accomplish feature based registration. But, feature based
registration has some limitations as well as advantages. The proposed method employs
feature based registration technique to obtain a coarsely registered image which can be given
as input to intensity based registration technique to get a fine registration result. It helps to
reduce the limitations of intensity based technique. i.e. it takes less time for registration. To
achieve this task, the mutual information is selected as similarity parameter.
Mutual information (MI) is used widely as a similarity measure for registration. In order to
improve the robustness of this similarity measure, spatial information is combined with
normalized mutual information(NMI). MI is multiplied with a gradient term to integrate
spatial information to mutual information and this is taken as similarity measure. The
registration function is less affected if sampling resolution is low. It contains correct global
maxima which are sometimes not found in case of mutual information. For optimization
purpose, Fast Convergence Particle Swarm Optimization technique (FCPSO) is used. In this
optimization method, the diversity of position of single particle is balanced by adding a new
variable, particle mean dimension (pmd) of all particles to the existing position and velocity
equation. It reduces the convergence time by reducing the number of iterations for
optimization.
vii
TABLE OF CONTENTS
CONTENTS PAGE NO.
Acknowledgement……………………………………………………………………………v
Abstract………………...…………………………………………………………….………vi
List of Figures…………………………………………………………………………..........ix
List of Tables…………………………………………………………………………..…….xi
List of Abbreviations……………………………………………...……………………..…xii
1. Introduction……………………………………………………………………………....2
1.1. Overview………………………………………………………………….……....2
1.2. Image Matching Techniques……………..………………………………...….….3
1.3. Motivation…………………………………………………….…………………..3
1.4. Objective….…………………………………………………….…………….…..4
1.5. Thesis organization…………………………………………………..…………..5
2. Literature Survey………………………………………………………………………...7
3. Registration of Medical images using Contour information and Mutual
information.......................................................................................................................10
3.1. Introduction……………………………………………………………….…….10
3.2. Flow Chart………………………………………………………………….…...10
3.3. Course Registration……………………………………...…………………...….12
3.4. Fine Registration……………………………………………………………..….15
3.5. Results and Discussion…………………………………………………..………15
3.6. Conclusion………………………………………………………………….…....23
4. Intensity based rigid registration of medical images…………………………………25
4.1. Introduction…………………………………………………………………..….25
4.2. Flowchart……………………………………………………………………..….26
4.3. Method…………………………………………………………………….….…27
4.3.1. Mutual Information…………………………………………………….......27
4.3.2. Including gradient information………………………………….……........28
4.3.3. Optimization..................................................................................................29
4.3.4. Fast Convergence Particle Form Optimization..............................…...........31
4.4. Results and Discussion.…….………………………………………………..…..33
4.5. Conclusion…………………………………………………………………….....38
viii
5. Conclusion…………………………………………………………………………….....40
5.1. Conclusion…………………………………………………………………..…...41
5.2. Suggestions for Future Work………………………………..……………....…..42
References………….…………………..……………………………………………………43
Dissemination…......................................................................................................................46
ix
LIST OF FIGURES
FIGURES PAGE NO. 3.1. Flow chart for image registration using contour information and mutual information….11
3.2. Registration between CT Images for up-scaling………………………………………...16
3.2(a) Reference image…………………………………………………………….....16
3.2(b) Float image…………………………………………………………………....16
3.3. Coloured images…………………………………………………………………………17
3.3(a) Reference Image(red)……………………………………………...…………..17
3.3(b) Float Image(green)………………………………………………...…………..17
3.4. Edges of Images………………….……………………………………………………...17
3.4(a) Edges of reference image............................................................................…...17
3.4(b) Edges of input image………....…………………...…………………………..17
3.5. Contour of images……………………………………………………………………….18
3.5(a) Contours of reference image…………………...……………………………...18
3.5(b) Contours of input image…………………………...………………………….18
3.6 Rotated input image………………………………………..………...…………………..18
3.7. Boundary of images……………………………………………………………………..19
3.7(a) Reference image……………………………………………………………….19
3.7(b) Rotated input image…….…………………………………..…………………19
3.8 Scaled input image…………………………………………………………...................20
3.9 Coarse registration result after translation of scaled image……………………...………20
3.10 Input Images for fine registration……………………………………………………….21
3.10(a) Reference Image……………………………………………………………..21
3.10(b) Input image after coarse registration………………………………………...21
3.11 Final registered image…………………………………………………………………..21
3.12. Set of two CT Images.……………………………………………………………….…22
3.12(a) Reference Image….……………………………………………………….…22
3.12(b) Float Image……….……………………………………………………….…22
3.13. Registration Results…………………………………………………………………….22
3.13(a) Coarse Registration….………………………………………….……………22
3.13(b) Fine Registration…….………………………………………….……………22
4.1. Flow chart of the method………………………………………………………………..26
x
4.2. Particle mean dimension for n particles……….……………….………………………..31
4.3. CT images……………………………………………………………………………….33
4.3(a) Reference Image………....…………………………………………………....33
4.3(b). Float Image………..…...……………………………………………………..33
4.4. Coloured CT images……………………………………………………………………..34
4.4(a) Reference image(red)……………….…………………………………………34
4.4(b). Float image(green).………………………...….……………………………...34
4.5. Registered image…………….……………………...…………………………………...34
4.6. MRI images……………………………………………………………………………...35
4.6(a). Reference Image…...………………………………………………………....35
4.6(b). Float Image….………………………………………………………………..35
4.7. Coloured MRI images…………………………………………………………………...35
4.7(a). Reference image(red)….……………………………………………………...35
4.7(b). Float image(green)…….………………….………………………………......35
4.8. Registered image……………………………….……………………………..................36
4.9. CT and MRI image……………………………………………………………………....36
4.9(a). Reference Image….………………………………………………………......36
4.9(b). Float Image…………….…………………………………………………......36
4.10. Coloured CT and MRI images…………………………………………………………37
4.10(a). Reference image(red)….……………………………………………….……37
4.10(b). Float image(green)…….…………….………………………………….…...37
4.11. Registered image….……………………………………………………………….…...37
xi
LIST OF TABLES
TABLES PAGE NO.
I. Coarse registration parameters…………………………………………………...23
II. Fine registration parameters……………………………………………………...23
III. Parameters with standard PSO…………………………………….……………..37
IV. Parameters with FCPSO…………………………….…………………………...37
xii
LIST OF ABBREVIATIONS
MI : Mutual Information
NMI : Normalized mutual information
ECC : Entropy Correlation Coefficient
PSO : Particle Swarm Optimization
FCPSO : Fast Convergence Particle Swarm Optimization
1
CHAPTER 1
INTRODUCTION
Contents
Overview
Image Matching Technique
Motivation
Objective
Thesis organization
2
INTRODUCTION
Registration of images is the bringing of the images into a single coordinate system for its
further analysis. It is also known as image alignment i.e. the two different images in different
local coordinates have to be aligned in a single coordinate. One of the images is chosen as
reference image and another image or the float image will be registered according to the
coordinates of reference image.
1.1. Overview
In image processing, when we try to combine the details of the images, we are actually search
for the relation between two or more images. The study of this relationship usually becomes
manageable once a resemblance is set up between the images. The task of setting up this
correspondence is known as registration of images.
Image registration is the task of matching two or more partially overlapping images taken at
different time instants or from different observation points. It is a basic image processing
technique which is very important step to integrate information from various sensors. It helps
to find changes in images which are taken at different time instant. It helps to deduce three-
dimensional information from stereo images and to identify model-based objects.
The systems in which image registration is a important constituent includes matching a target
with a real-time image of a scene for target recognition, land utilization observation using
satellite images, stereo image matching to get shape for autonomous navigation, and
alignment of multimodality images for identification of diseases. Image registration is an
initial footstep for various applications such as remote sensing and multi-sensor fusion based
target recognition. It is required earlier to image fusion or image mosaic.
Registration is done manually as well as automatically[1]. In manual registration, images
which are to be registered is taken and human operators manually select corresponding
features. For accurate registration results, operators have to choose a plenty of pairs of feature
over the full images, which is laborious as well as subjected to irregularity and bounded
accuracy. Therefore, it is necessary to find automated techniques which need less or no
operator supervision.
3
1.2. Image Matching Techniques
Image matching techniques can be categorized as gray-scale based matching or image feature
based matching.
Gray scale-based matching: Gray scale-based matching examines images as two
dimensional signals and make use of statistic approaches to find the correlation functions
among signals [2-4], and then obtain their resembling and homonymy points. Gray-scale
techniques give good results but take more time as compared to feature based techniques.
Feature-based matching: Feature-based matching finds some features within the images
such as points, lines, surfaces and planes [5][6], and then defines properties of those features
and then matches the images according to these characteristics. The similar features which
are used are textures, shapes and spatial positions. It involves only partial pixels and, thus,
reduces matching computation. It gives good registration accuracy because of location
sensitivity of the matching properties. The feature extraction lessens the noise effects and
increases the compliance with changes in intensity values, morphing and occlusion. The
feature based techniques gives less accurate results as compared to intensity based technique.
1.3. Motivation
Edges in the images can be detected very easily in the images. Thus, using these edges some
features can be obtained by which we can accomplish feature based registration. But feature
based registration has some limitations like low accuracy as well as advantages like less time
consuming. Thus, a method was to be searched which employs feature based registration
technique to obtain a coarsely registered image which can be given as input to intensity based
registration technique to get a fine registration result. The problem with intensity based
registration is that it is time consuming. So, the method was required which helps to reduce
the limitations of intensity based technique. i.e. it takes less time for registration.
As mutual information may sometimes leads to incorrect registration in intensity based
technique, normalized mutual information is taken as search parameter in the next technique
as this measure is does not vary with the overlapped area between the images. To make the
measure more informative and to make the measure more robust, spatial information is
included in the similarity measure to incorporate the intensity information of neighboring
pixels. Particle Swarm Optimization (PSO) is a simple and computationally efficient
4
optimization method. Many modifications have been suggested to the standard particle
swarm optimization to find good and faster solutions than the evolutionary algorithms, but
those modifications may got stucked in poor region or result in divergence to unstable
situations. Thus, modification in the optimization technique was required to avoid this
problem and make the optimization process fast.
1.4. Objective
The objective of this work is to develop efficient method of registration of the medical
images which uses images‟ contour information as well as mutual information i.e. a
registration method which is a combination of feature based and intensity based method.
The next objective is to develop an effective intensity based registration technique which has
sufficient information in the similarity measure and also to reduce convergence time in case
of global optimization of this measure.
1.5. Thesis Organization
Including this introductory chapter, the thesis is divided into six chapters:
Chapter 2: Literature Review
In this chapter, we discuss about the literature survey carried out related to the work.
Chapter 3: Registration of medical images using contour information as well as mutual
information
In this chapter, registration of medical images is discussed. The images are rotated, scaled
and translated with respect to each other. The algorithm uses combination of feature based
and intensity based technique. It discusses the steps involved in the algorithm. Also the
results and discussions have been given in this section.
Chapter 4: Intensity based rigid registration of medical images
This chapter describes a method to register images using modified normalized mutual
information and Fast Convergence PSO optimization. Moreover, it consists of results and
discussions.
5
Chapter 5: Conclusion
This chapter is concluded with the important points of the research work. Furthermore, some
suggestions for future work are given.
6
CHAPTER 2
LITERATURE SURVEY
7
LITERATURE SURVEY
A lot of work has been done in the field of image registration. The following is a brief
introduction of some of the papers.
B.Zitova and J.Flusser presents a basic overview of image registration methods[1].
R.Suganya, Dr.S.Rajaram and K.Priyadharsini used centre of gravity the images for initial
registration of images and final registration is accomplished by maximizing the mutual
information[2]. L.Junli, C.Rijuan, J.Linpeng and W.Ping proposes a weighted mutual
information (WMI) for registration of medical images by which doctors can weightage to the
image according to which registration has to be done[4]. I.Misra, S.M.Moorthi, D.Dhar and
R. Ramakrishnan proposes an automatic registration method for remotely sensed
multispectral images. The method works even if float and reference images are from different
sensors[5]. C.S.Qiao uses an image matching technique based on feature extractor such as
Harris Operator and proposed a new corner point matching method based on the singular
value decomposition[6]. J.Hu, Y.Yang and Z.Su proposes a rapid registration method of the
medical images done by using multi-scale transform and contour line[7]. N.A. Al-Azzawi,
H.A.M. Sakim, W.A.K.W. Abdullah describes the standard PSO algorithm which is used in
the paper to optimize MI. PSO is a global optimization algorithm[8]. F. Maes, A. Collignon,
D. Vandermeulen, G. Marchal, and P. Suetens proposes mutual information of the images as
the matching parameter and used MI to measure the statistical dependency in the images or
redundant information in the image gray values of the corresponding pixels in couple
images[10]. L. Ding, A. Goshtasby, and M. Satter proposes a method of registration by
selecting templates i.e. subimages from an image and locating the same template in another
image of the same view and selecting the centroids of the templates as the control points [11].
J.P.W. Pluim, J.B.A. Maintz and M.A. Viergever gives a survey of various methods
involving mutual information and the various classification of the image registration
methods. They explained various advantages and disadvantages of taking mutual information
as a measure and explains various methods which eliminates the drawback of MI [12]. C.
Studholme, D.L.G. Hill and D.J. Hawkes proposes a normalized measure which is invariant
to overlapping areas between the images. It is the ratio of the addition of the individual
8
entropies and the joint entropy[13]. C.Studholme, D.L.G.Hill and D.J.Hawkes proposes a
method of registration by computing mutual information of a pair of images by labelling one
of the images i.e. labelling of connected region within the images which helps to maintain or
increase the measure [15]. J. P.W. Pluim, J.B.A. Maintz and M.A. Viergever describes how
gradient information can be included in a similarity measure to increase the information
content in the similarity measure[16]. J. Xie , Z. Chen, G. Xu proposes a method to find
feature points by wavelet multiscale product and mutual information is used to register
feature points and used particle swarm optimization technique to obtain registration
parameters[17]. A. Sahu, S. K. Panigrahi, S. Pattnaik proposes a Fast Convergence Particle
Swarm Optimization (FCPSO) method which balances the diversity in the position of a single
particle by defining a new variable which is the average of the locations of all dimensions of
every particle. It improves the functioning of PSO [18].
9
CHAPTER 3
REGISTRATION OF MEDICAL IMAGES USING
CONTOUR INFORMATION AS WELL AS
MUTUAL INFORMATION
Contents:
Introduction
Flow Chart
Course Registration
Fine Registration
Results and Discussion
Conclusion
10
REGISTRATION OF MEDICAL IMAGES USING
CONTOUR INFORMATION AS WELL
AS MUTUAL INFORMATION
3.1. Introduction
The medical image provides the various details of the patient. It helps a doctor in
identification of any disease developed in the patient. In the applications of the medical
images, the medical image registration is an important technique because it helps a doctor to
observe the development of the disease during some time duration and it also helps a doctor
to take an accurate and proper treatment scheme about the disease.
Image registration techniques can be based on intensities or gray-scale of images and features
selected in the images whichever is used in registration. Feature based registration results in
coarse registration. By using some intensity based method, we can get a fine or accurate
registration result. Thus, a method of registration of the medical images based on contour
information as well as mutual information of images is proposed.
Feature based registration gives a coarse result due to involvement of partial pixels. Thus,
using some intensity based method, a fine or accurate registration can be obtained [7]. This is
a registration method for medical images based on contour lines of images and mutual
information. First of all, a coarse registration is obtained using image contour lines obtained
from canny detector and then fine registration is accomplished using mutual information
maximization.
3.2. Flow Chart
Fig 3.1 shows the flow chart for image registration using contour information and mutual
information.
11
Slave (input image) Target (reference image)
Edges detection
Contour detection
Included angles
Registered Image
Translation of centres
Course registration result
Maximization of MI
Slope of principal axis
Centre detection
Fig 3.1 Flow chart for image registration.
12
3.3. Coarse Registration
Coarse registration of image is accomplised by using feature based registration method.
A. Contour Line Extraction
The medical images like brain are rigid in nature, and their edge characteristics are very clear.
So extraction of contour of images is easy. Brain images are taken as an example of medical
images. Edges of an image are regions with strong intensity contrasts. Detection of edges
decreases the quantity of data significantly and removes useless information, and preserves
the important structural qualities of an image.
Edge Detection:
Contours of medical images to be registered can be easily extracted by the use of Canny
operator. Canny operator, which is known as optimal edge detector, extracts images‟ edge
distinctly and precisely even in the noisy environment. It provides thin edges.
Contour Extraction:
Now, contours of images can be obtained from the edge images which are obtained by using
Canny operator by using line by line scanning method. Every row of the edge images are
scanned from first to last pixel and only first and last non-zero pixel will be selected. This
gives us the contour information of the rows. Similarly for contour information of the
columns, every column of the edge images are scanned from first to last pixel, and only first
and last non- zero pixel will be selected. Thus, the contour information of a medical image is
obtained.
B. Coarse Registration based on contour information of images
Rotation Correction:
Let the pixel coordinates of an images‟ contour line be {( ,i ix y ) i =1, 2,…n}, where n
denotes total number of pixels of the contour line. Thus, the centre coordinate of an image
can be calculated as given in equation (3.1),
13
1
1
1
1
n
i
i
n
i
i
x xn
y yn
(3.1)
where,
( x , y ) represent the centre coordinates of the images i.e.
( rx , ry ) represent the centre coordinate of the reference image and
( fx ,fy ) represent the centre coordinate of the float image.
Rotation angle can be obtained by finding the principal axes of the couple medical images.
The inertia matrix of contour line of images can be set as given in equation (3.2),
11 12
21 22
u uI
u u
(3.2)
where,
2
11
1
( )N
i
i
u x x
2
22
1
( )N
i
i
u y y
12
1
( )( )N
i i
i
u x x y y
Based on the inertia matrix calculated by using (2), long and short axes of the images can be
found because these axes are actually the two eigenvectors of the inertia matrices. Now, the
included angles between the two long axes and the two short axes can be found respectively a
as given by equation (3.3),
1
1
1
2
) ( (1,2)* (1,2) (2,2)* (2,2)
( (1,1)* (1,1) (2,1)* (2,1))
r f r f
r f r f
Cos V V V V
Cos V V V V
(3.3)
14
where rV represents eigen vectors of the reference image inertia matrix and fV
represents
eigen vectors of the float image inertia matrix. The initial rotation angle is obtained by the
averaging the two included angles as given in equation (3.4).
Based on the initial rotation angle, float image can be rotated.
Scaling Correction:
Again the inertia matrix for the rotated float image is calculated by repeating the above
procedure. Let 'fV be eigen vectors for rotated float image. Then, the slope of the eigen
vectors of newly calculated inertia matrix of rotated float image and eigen vectors of
reference image is calculated by equation (3.5),
1 2,1 / 1,1
2 2,2 / 1,2
m V V
m V V
(3.5)
Principal axes can be plotted for both images as principal axis passes through centre
coordinate ( x , y ) and slope of the axes have been obtained. Shift the principal axes in both
directions, till this axes just touches the object boundary and thus, boundaries of the object is
drawn by the rectangle enclosing the images. By calculating the difference between the
values of those shifts, width and height of the object is obtained. The ratio of width of
reference to rotated float image gives the scaling factor in y-direction and ratio of height of
reference to rotated float image gives the scaling in x-direction. The rotated float image will
be scaled by the obtained scaling factor. Now, scaled image is same of same size as the
reference image.
Translation Correction:
Again the centre coordinates '' ''( , )f fx y of scaled float image can be calculated. Now, the
translation parameters between the images is calculated as given by equation (3.6),
''
''
f r
f r
x x x
y y y
(3.6)
15
According to this translation value, the coarse registration of the pair of medical images has
been done.
3.4. Fine Registration
Mutual information (MI) is very popular similarity parameter which is based on Shannon
entropy and is widely used in the medical imaging domain. The mutual information is a
statistical measure of the mutual dependence of the two images i.e. it represents the statistics
correlation of two sets of image data. Registration is assumed to be done when mutual
information is maximum i.e. the images should be aligned such that the quantity of
information they have about each other is maximum. The mutual information of two images
A and B is calculated as given in equation (3.7).
I (A, B) = H (A) + H (B) – H (AB) (3.7)
where, ( ) ( ) log ( )A AH A P a P a
H(A) denotes the entropy of image A and the joint entropy H(AB) can be calculated as,
, ,( ) ( , ) log ( , )A B A BH AB P a b P a b .
Larger the value of the mutual information obtained in the registration technique, the more
precise registration results are obtained.
So, varying the input image over a range of angles, a set of translation is checked for rotated
image with respect to input image and the value of translation and rotation for the maximum
value of mutual information is noted. Now, the resultant image of coarse registration is rotated
and translated by that amount to get fine registration result.
3.5. Results and Discussions
The reference and slave image consists of 256 intensity values i.e. 8 bits gray-scale medical
images. Example 1 shows the registration of set of two CT images for up-scaling. Example 2
shows the registration of the set of two CT images for downscaling.
16
Fig. 3.2 represents the set of two CT images taken for registration. Fig. 3.3 represents the same
images which are coloured just to recognize. Fig. 3.4 represents the edge images. Fig. 3.5
represents the contours of images obtained from edge images. Fig.3.6 shows the rotated input
image. Fig. 3.7 represents the boundary of images. Fig.3.8 shows scaled input image. Fig. 3.9
represents coarse registration result after translation of scaled image. Fig. 3.10 represents the
images after coarse registration. Fig. 3.11 shows the final registered image.
Fig. 3.12 represents the two brain images taken for registration. Fig. 3.13 shows the
registration results.
Example 1:
Registration between CT Images for upscaling
(a) (b)
Fig. 3.2. (a) Reference Image (b) Float Image
17
(a) (b)
Fig. 3.3.(a) Reference Image coloured as red (b) Float Image coloured as green
(a) (b)
Fig. 3.4 (a)Reference Image (b) Float Image
18
(a) (b)
Fig. 3.5. (a) Contour of reference Image (b) Contour of float Image
Fig.3.6. Rotated input image
19
(a) (b)
Fig. 3.7. (a) Reference Image (b) Float Image
20
Fig.3.8. Scaled input image
Fig.3.9. Coarse registration result after translation of scaled image
21
(a) (b)
Fig. 3.10 (a) Reference Image (b) Input image after coarse registration
Fig.3.11. Final registered image
22
Example 2:
Registration between CT Images for downscaling
(a) (b)
Fig. 3.12 (a) Reference Image (b) Float Image
(a) (b)
Fig. 3.13 (a) Coarse Registration (b) Fine Registration
23
The registration parameters obtained in the two examples of registration are given in Table I
and Table II.
Table I. COARSE REGISTRATION PARAMETERS
Example Rotation
(in degrees)
Scaling Translation
Sx Sy x Y
1 18.78 1.31 1.31 145 249
2 19.34 0.693 0.697 12 34
Table II. FINE REGISTRATION PARAMETERS
Example Rotation
(in degrees)
Translation Maximum MI
x y
1 -4 12 11 1.7
2 -2 14 26 1.14
This method is a combination the feature and intensity information of the images. So, it
involves less mathematical complexity. In feature-based method, partial pixels are selected
and thus, calculations are reduced and in intensity-based method, mutual information is to be
calculated over a small range of angles as the course registration gives us an approximate
result.
3.6. Conclusion
A method of registration of the medical images based on contour information and mutual
information of the images is proposed. The feature as well as intensity information of the
images are used effectively in the proposed work. The result shows that the proposed
approach involves less complexity and is an effective medical image registration method.
24
CHAPTER 4
INTENSITY BASED RIGID REGISTRATION
OF MEDICAL IMAGES
Contents
Introduction
Flowchart
Method
Mutual information
Including gradient information
Optimization
Fast Convergence Particle Form Optimization
Results and Discussions
Conclusion
25
INTENSITY BASED RIGID REGISTRATION
OF MEDICAL IMAGES
4.1. Introduction
Mutual information is an gray-scale based similarity parameter used in case of both
monomodal as well as multimodal images[8][9][10][11]. It does not require any features such
as points or surfaces as feature based registration technique which leads to coarse registration.
In spite of the promising results given by mutual information, sometimes it results in
misregistration of images i.e. it fails occasionally. This occurs when the resolution of the
images is low, when little information is present in the images or when there is less overlapping
region between the images. The mutual information measure is influenced by size of the
overlapping part of the images in two ways[12]. Decreasing the overlap area decreases number
of samples. If number of samples reduces, it reduces the statistical power of probability
distribution estimation. Futhermore, if misregistration rises, the mutual information measure
can become high because increasing misregistration matches with reducing overlap. This
happens when the corresponding area of object and background becomes equal and the sum of
the marginal entropies increases rapidly in comparison to joint entropy. A normalized measure
of mutual information is proposed by Studholme [13]. Normalised mutual information(NMI) is
less affected by changes in overlap and is expressed by equation (4.1).
Improved results are obtained if normalized measure is taken for rigid registration of
multimodal images[13].
In mutual information found from Shannon entropy[14], the dependence of the intensity values
of the adjacent pixels is completely neglected. But, the original Shannon entropy definition
includes the dependence of prior signals. However, the definition of Shannon entropy used in
applications is for independent consecutive signals. This idea of independence of signals does
not apply in case of medical images. The dependence of the intensity values of adjacent pixels
is actually termed as spatial information of the images. Thus, including the spatial information
26
with mutual information[15] can improve registration results. So, to integrate spatial
information, mutual information can be combined with parameter obtained from the gradients
at corresponding points. This parameter aligns gradient vectors of large magnitude and of same
orientation[16].
Particle Swarm Optimization(PSO) is a global optimization technique which is widely
used[17]. But, it takes large time to converge. So, to reduce the number of iterations, Fast
Convergence Particle Swarm Optimization[19] is used in this method.
4.2. Flowchart
Flow chart of the method is given in figure 4.1.
No
Yes
Fig.4.1. Flowchart of method
Start
Random starting locations and velocities
Evaluate fitness function
Fitness output is compared to obtain Pbest
Fitness output is compared to obtain Gbest
k 1 1. 1. –
2. 2. – 3. 3. –
ij ij ij ij
i ij
v wv c rand pbest x
c rand gbestj xij c rand Pmd
k k k
k k k kx
and 1 1ij ij ijx t x t v t
If Gbest remains
constant for 15
iterations
Stop
27
4.3. Methodology
The method used is the combination of the combined measure of normalized mutual
information as well as the gradient information and the technique used for optimization
purpose.
A. Mutual information
Mutual information of the two images is the addition of the individual and joint entropies of
the two images. Entropy is, how much the probability distribution of the images disperses.
When a probability distribution has acute and dominant peaks, entropy will be minimum.
When every outcome has equal chances of occurring i.e. for a uniform distribution, entropy
will be maximum. By arranging the probability distribution of the images intensity values,
the entropy of the images is calculated. The Shannon entropy for probability distribution is
defined as given in equation (4.2),
,
( , j) logp(i, j)i j
H p i (4.2)
i.e. H(A) denotes the individual entropy of image A and
H(B) denotes the individual entropy of image B and are calculated as given by equation (4.3)
and (4.4),
(A) (a) log (a)A AH P P (4.3)
(B) (b) log (b)B BH P P (4.4)
H(A,B) is the joint entropy of image A and image B, i.e. the entropy of the joint probability
distribution of the intensities of image A and image B.
By computing a normalized joint histogram of the intensities of the two images, joint
probability distribution is estimated. It is expressed as given in equation (4.5).
, ,( , ) ( , ) log ( , )A B A BH A B P a b P a b (4.5)
The mutual information I(A,B) of two images A and B intermingles the individual and joint
entropies of the images and is given by equation (4.6).
28
I(A,B) = H(A) + H(B) − H(A,B) (4.6)
Images are correctly registered when MI of images is maximum. This suggests, there should
be a balance between joint entropy minimization and marginal entropies maximization. The
joint entropy will be minimized if the joint distribution is minimum dispersed, i.e. when a
distribution has less number of acute and dominant peaks. This coincides with registration. In
case of improper alignment of the images, new pairs of grey values will be introduced which
decreases the probabilities of the „correct‟ combinations resulting in more dispersed joint
probability distribution. But, the mutual information measure is affected by overlapping areas
between the images and normalized MI can overcome this problem[12] and the entropy
correlation coefficient(ECC) is different form of normalised MI given in equation (4.7),
B. Integrating gradient information
Image areas with strong intensity contrasts are the areas of high information value as it
denotes transition of tissues. The gradient is computed on spatial domain. Normalised mutual
information is modified to integrate spatial information existing in the images. i.e. normalised
mutual information is multiplied with a gradient term. This term is based on both the
magnitude and the orientation of the gradient vectors[16]. Directly calculating normalized
mutual information of gradient images can also be done to incorporate spatial information.
But, it can result in narrow attraction range of registration function and a lot of information of
the intensity values is rejected. Thus, a combination of normalised mutual information i.e.
Entropy Correlation Coefficient and spatial information is used. The gradient vector is
calculated for every sample point „a‟ in one image and the corresponding point „b‟ in another
image, which is obtained by geometric transformation of „a‟. The gradient vector is obtained
by calculating two partial derivatives in both x and y direction. To find the gradient vector,
the image is convolved with the first derivatives of a Gaussian kernel of scale σ. σ can be
taken in range of 0.5 to 1. The angle , ( )a b within the gradient vectors can be calculated as
given by equation (4.8),
29
,
a( ). b( )( ) arccos
( ) b( )a b
a
(4.8)
with ∇a(σ) denotes the gradient vector at point a of scale σ and mode denotes magnitude.
In different modality images, the various tissues have different intensities. So, the gradient of
the images points in dissimilar directions. However, since the different modality images
represent the identical anatomical structures, gradients of the two multimodal images will
have the same orientation; either it can be in same or reverse directions. Weighting function
w is used so as to adjust both very small angles as well as large angles that nearly equals 180
and is given by equation (4.9).
,
,2 ( ) 1 ( )
2
b
a b
acosw
(4.9)
But, because of difference in imaging processes of different modalities, it is not essential that
different modality images represent the same transitions of tissues. Therefore, strong
gradients in a certain modality may not be present or less significant in another modality.
But, we have to include strong gradients of the both images. Thus, minimum of the gradient
magnitudes is multiplied by the angle function. Gradient term is the summation of the
resulting product for all samples which is multiplied by the normalised mutual information
measure. Tissue transitions in both modalities are emphasized. Gradient term may be
mathematically expressed as given by equation (4.10),
(a
,
, ) ( )b
, * (| | | ), |a b
A B
G A B w min a b
(4.10)
The combined measure of normalized MI and spatial information is given by equation (4.11).
ECCnew (A, B) = G(A, B)*ECC (A, B) (4.11)
C. Optimization
Particle Swarm Optimization[18] is a population-based search technique. Particle Swarm
Optimization is both simple and effective. Particles represent a population of possible
solutions. Particles are depicted by a position and a velocity vector both. The location of each
particle represents a solution. The main logic is that individuals or particles gain experience
from the member or particles at the best position to reach the group objective or to reach the
30
location where there is maximum availability of food. As the population moves towards its
objective, each individual adjusts its position according to its own and the adjacent particles
experiences. A fitness function is used to search for the best position. The fitness function
must be defined by the parameters to be optimized. Every time the loop repeats in simulation,
the fitness function can be computed by taking the location of the particles in the search
space. Every particle stores the best value found by it so far. The location of the highest
fitness value of each particle is called personal best or local best (pbest). The location of the
highest fitness value among the particle swarm i.e. among all particles is called global best
(gbest). In each iteration, there is exactly one gbest and all the particles are pulled in the
direction of gbest location. After finding pbest and gbest values, the particle modify the
velocity and position as given by two equations (4.12) and (4.13).
1 * ( ) 1* 1* ( ) 2*( 2* ( )) ( )ij ij ij ij j ijv k w v k c rand pbest x k c r gbest x k (4.12)
and
1 ( ) 1ij ij ijx k x k v k (4.13)
where,
1ijv k is the particle‟s velocity i.e. velocity of ith particle at (k + 1)th iteration,
( )ix k is the solution of current particle i.e. position of ith particle,
ipbest is the previous best position of the ith particle,
gbest is the global best position achieved by particle swarm till then,
rand1 and rand2 are random numbers between 0 and 1,
c1 is the cognitive factor or individual learning rate,
c2 is the social constant,
w is the inertia weight,
k is number of iteration i.e. k = 1,2,…,
j is the particle dimension.
To control the velocity of a particle, a maximum velocity maxv is inflicted on particle's
velocity i.e. if any particle moves with a velocity that exceeds the maximum velocity maxv,
then that particle‟s velocity is reduced to maxv. Each velocity vector is compressed within the
limits [ maxv , minv ] to lessen the chances that the particle departs from the position limits.
31
D. Fast Convergence-Particle Swarm Optimization
In standard PSO, starting particles are evenly dispersed in the search space. The method may
get confined in local minima and ipbest may not get changed for many steps, because of the
mutual limitation of variable of each dimensions. It is difficult for the method to run away
from the local minima, thus, the correct location will not be obtained.
When the swarm gets updated from the k generation to k + 1, along with the trace of ipbest
and gbest, the particles can trace ipmd which is obtained from the swarm. The new variable
ipmd of ith particles are calculated as given by equation (4.14).
Pmd1
Pmd2
Pmd3
PmdN
Fig.4.2. Particle mean dimension for n particles
1 2 .. / i i i iDPmd x x x D (4.14)
where,
D, Particles‟ dimensions in the swarm and the new velocity and position is represented by
equation (4.15) and (4.16) respectively,
k 1
1. 1. –
2. 2. –
3. 3. –
ij ij
ij ij
j
i ij
v wv
c rand pbest x
c rand gbe
k
k k
k kst xij
c rand Pmd k kx
(4.15)
1 1ij ij ijkx k x v k (4.16)
X11 X12 X13………………….X1n……X1D
X21 X22 X23………………….X2n……X2D
X31 X32 X33………………….X3n……X3D
XN1 XN2 XN3………………….XNn……XND
32
where,
c3 is the mean best learning factor,
rand3 is the random vector between [0, 1].
Here, c1,c2 and c3 are selected satisfying the equation (4.17).
= c1 + c2 + c3 (4.17)
where, >= 4
After adding ipmd in the velocity formula, all ipbest , gbest and ipmd gives information to
the next generation combinely and thus, the information received from previous generation
increases. This method helps to get the favourable solution quickly. Also, the weightage
factor of ipmd , i.e. „c3‟ is small. Thus, this term equals disturbance information and
increases the diversity between the particles. The gbest location improves convergence rate.
However, it decreases the diversity among population which results in local minima.
Simultaneously, parameter ipmd takes the particles to a better location and reduces the
chance of attraction of particles towards local minima.
E. Formulation of FCPSO
First of all, some particles are chosen and the number of dimensions for which float image is
to be corrected is decided. The experiments are performed by taking 25 particles and 3
dimensions are to be searched i.e. rotation in one plane and translation along two axis. Search
space is the limits for the position of particles in which food is to be searched. Search space
for particles position is given as [-48 48; -48 48; -25 25] where first column shows minimum
limit and second column shows maximum limit for particles position in each dimension. The
value of [ maxv , minv ] is selected as twice the limits of position for each dimension.
Cognitive(c1) and social constant(c2) are given as 1.8 and c3 as 0.4. The particles are
allocated random positions at first. The fitness function i.e. ECCnew measure is calculated
for those particle locations. The location for the best availability of food i.e. maximum fitness
function is saved as gbest and for each particle pbest i.e. the location of best food availability
is saved as the initial particle location at first run. The value of pmd is calculated for each
generation of particle. The velocity for the particles is calculated by using equation (4.15). If
the velocity of the particle obtained is greater than maxv , then it is set to maxv and if it is less
than minv then, it is set to minv .The new locations for the particles are calculated by using
33
equation (4.16). The fitness function output is then checked. If the new locations give high
value then, according to that pbest and gbest are set. The loop was repeated until gbest
remained constant for 15 iterations.
4.4. Results and Discussion
The target and slave image consist of 256 intensity values i.e. 8 bits gray-scale medical
images. The floating image has some translation and rotation with respect to reference image.
Three examples of registration are given. First two examples are for monomodal images and
third example is of multimodal registration. Example 1 gives the registration of two CT
images. Example 2 gives the registration of two MRI images. Example 3 gives the registration
of CT and MRI images.
Fig. 4.3 represents the set of two CT images taken for registration. Fig. 4.4 represents the same
images which are coloured just to recognize. Fig. 4.5 shows the registered image. Fig. 4.6
represents the set of two MRI images taken for registration. Fig. 4.7 represents the same MRI
images which are coloured just to recognize. Fig. 4.8 shows the registered image. Fig. 4.9
represents the CT and MRI images taken for registration. Fig. 4.10 represents the CT and MRI
images which are coloured just to recognize. Fig 4.11 shows the registered image.
Example 1: CT images
(a) (b)
Fig. 4.3. (a) Reference image (b) Float image
34
(a) (b)
Fig. 4.4. (a) Reference image coloured as red (b) Float image coloured as green
Fig. 4.5
35
Example 2: MRI images
(a) (b)
Fig. 4.6 (a) Reference Image (b) Float Image
(a) (b)
Fig. 4.7. (a) Reference Image with red (b) Float Image with green
36
Fig.4.8
Example 3: CT and MRI image
(a) (b)
Fig. 4.9. (a) Reference Image (b) Float Image
37
(a) (b)
Fig. 4.10. (a) Reference Image with red (b) Float Image with green
Fig. 4.11
38
Parameters obtained after registration are given in Table III and IV.
Table III. PARAMETERS WITH STANDARD PARTICLE SWARM OPTIMIZATION
Eg. Maximum
ECCnew
No. of
iterations
RMSE
CT-CT 1.39e+05
1275
0.675
MRI-MRI 1.61e+05
1225
1.85
CT-MRI 1.69e+04
1200
8.32
Table IV. PARAMETERS WITH FAST CONVERGENCE PARTICLE SWARM
OPTIMIZATION
Eg. Maximum
ECCnew
No. of
iterations
RMSE
CT-CT 1.29e+05
725
0.973
MRI-MRI 1.21e+05
825
2.78
CT-MRI 1.67e+04
525
8.33
This method is based on intensity values of images. The numbers of iterations get reduced in
case of Fast Convergence Particle Swarm Optimization while the result accuracy is
approximately same. The number of iterations is reduced to almost two third in case of
FCPSO than standard PSO. Thus, time complexity reduces and also, it reduces the chance of
attraction of particles towards local minima. RMSE is high in case of multimodal images as
the same part of images is represented by different intensity values.
4.5. Conclusion
A method of registration of the multimodal medical images based on normalised mutual
information and spatial information is proposed. The intensity information of images is used
effectively in the proposed work. As normalized mutual information is taken along with spatial
information, a measure has been found which is invariant to overlapping region and is more
robust measure than normalised mutual information as spatial information adds to the
information between the images. The combined measure gives a good registration function.
This registration function is less affected by if the sampling resolution is low. There are no
39
erroneous global maxima which can be obtained in case of mutual information. Also, local
minima caused by interpolations gets decreased.
The method uses a global optimization technique which is better than standard genetic
algorithms. Using Fast Convergence Particle Swarm Optimization, result can be obtained in a
lesser time than standard PSO. The proposed approach is, thus, more robust and is an
effective medical image registration method.
40
CHAPTER 5
CONCLUSION
Contents:
Conclusion Suggestions for Future Work
41
CONCLUSION
This chapter focuses on the advantages and limitations of all the methods used for image
registration. The scopes of future research work in this domain are also discussed.
5.1. Conclusion
Canny edge detector is the widely used edge detector as it gives thin edges. It is used in our
method for detection of the edges, which helps us to easily find the contours. Contours are
used for finding the principal axes of the medical rigid images. From principal axis
information, eigen vectors of the inertia matrix can be found. From these two eigen vectors,
the rotation angle can be found. Similarly to find scaling factor, these principal axes can be
shifted in both directions so as to enclose the medical structures within rectangles. From the
ratio of the heights and widths of the rectangle, scaling factors can be found in both
directions. Similarly, from the translation of the centres, translation between the images can
be found. This method takes very less time for computation and is time efficient. But, the
problem is that it does not give accurate result. The MI based fine registration overcame this
problem since it gives accurate result. As the input images to the MI based technique is
already coarsely registered, it takes very less time for computation and gives finely registered
images. This method is efficient and cheap but it can„t handle the images which are not rigid
structures. It works for rigid structures like brain. Also the images should have properly
defined principal axes to find out the scaling factor. Thus, a feature based registration gives a
course result as seen in chapter 3. Thus applying any intensity based can help us to increase
the accuracy of the method. At the same time, doing so would eliminate drawback of
intensity based technique (it takes large time to register the images) by reducing the search
space. Thus images‟ features and intensity information both are useful to find effective
registration techniques for medical images. The proposed approach involves less complexity
and is an effective medical image registration method.
The intensity information of images is used effectively in chapter 4. Mutual information
between the images is widely used as similarity measures in many intensity based registration
technique. But if the overlapping region between the images is less then MI may give an
incorrect measure. The normalised mutual information overcame this problem since it is
42
invariant to changes in overlapping region of the two images. The measure is made more
robust by including the spatial information by multiplying the gradient term with the
normalised measure. The combined measure helps in the correct object identification with
low probability of mismatch. For optimization, global optimization methods as better as
compared to local optimization methods like powell, simplex, gradient, etc as it does not
converge to into a local minima or maxima. And the method uses a global optimization
technique which is better than standard genetic algorithms. But, standard PSO takes large
time to converge. Number of iterations gets reduced in case of Fast Convergence PSO. The
number of iterations is reduced to almost two third in case of FCPSO than standard PSO. The
proposed approach is more robust, accurate and is an effective medical image registration
technique.
5.2. Suggestions for Future Work
A new method for feature-based registration can be searched for an overall increase in
registration performance. Different image similarity metrics can be used for refinement of
automatic image registration techniques for fine registration. Also, some more techniques can
be searched to further reduce the times of repetition in optimization technique of the
similarity measure. The input images used for the proposed method are the planar 2-D
images; it can be applied for the 3-D images as well.
43
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